If someone or something is familiar to you, you recognize them or know them well.
e.g. He talked of other cultures as if they were more familiar to him than his own...
e.g. They are already familiar faces on our TV screens.
Tony was unnerved by the uncanny familiarity of her face.
If you are familiar with something, you know or understand it well.
e.g. Lesinko is quite familiar with Central Television. He worked there for 25 years...
e.g. Most people are familiar with this figure from Wagner's opera.
The enemy would always have the advantage of familiarity with the rugged terrain.
If someone you do not know well behaves in a familiar way towards you, they treat you very informally in a way that you might find offensive.
e.g. The driver of that taxi-cab seemed to me familiar to the point of impertinence...
e.g. John's 'crime' was being too familiar with the manager and calling him Gouldy.
She needed to control her surprise at the easy familiarity with which her host greeted the head waiter.
'Gerald, isn't it?' I began familiarly.